Sounds like you're in for some fun upgrades! In your price range, I would certainly consider the new Polk L200 as well. I haven't heard them yet, but it's the successor to the highly praised LSiM line, and all reviews have been very positive so far. I'm on a list to hopefully get a demo around the end of the year/early next year. I'm hoping to get ears on them before the end of the year.
As for the phono preamp, I think this is often the most overlooked but highly important parts of the vinyl chain. The phonostage has to bring the very low signal from the stylus up to line level, which then feeds into your amp and the rest of the system. Your cartridge and TT are trying to extract as much information from the record as possible, and then the phonostage is trying to "expand" that information with as little interference or loss as possible. A lot of detail can be lost in the phonostage, and a lot of depth, tone, texture and detail can go with it. And anything that is lost (or added) from the phonostage will be amplified as the signal moves through the rest of your system.
Honestly, with what you are planning to purchase, I would put a decent budget aside for the phonestage. I don't want to give you a percentage or formula, because it's just not that simple. But don't under credit the phonostage. If you need to get something simple for budget reasons to get started, that's understandable, but you can get SO much more out of your TT with a good phonostage.
As for amps, you have some great options laid out. One thing to consider, is what all do you NEED your amp to do. For example, the CXA81 does not have a phonostage, so you would need to budget for that. But it does have a nice DAC, so you wouldn't need to budget for that.
The PM8006 does have a phonostage, but doesn't have a DAC. So do you need one?
The Halo Hint 6 has a DAC and a phonostage built in, so much more of a single box solution.
Other factors are balanced connections, sub outs, tape outs, headphone jacks, etc.
Personally, I like amps that don't have many features. Just let me select my input and amplify my sound. The Kinki Studio EX-M1 would fall in your price range, but no phonostage, no DAC, no sub outs, no BT, nothing. Just pure amplification. There are loads of other options too. I'm just making the point to find your key features of an integreated amp, and we can go from there. But you're off to a great start with the lineup so far. The only other thing I'd suggest is consider the MasterTracker vs UltraTracker if you're comfortable with the price difference. Getting it with the table is the cheapest you'll probably ever get it.